I'm pretty sure it's a question of fuel efficiency. Matter-antimatter is a pretty high energy, exotic form of power, but it does indeed consume fuel--matter is combined with equal amounts of antimatter, and the two annihilate and convert entirely (or almost entirely) into high energy photons, which are then used to perform whatever work needs to be done (in the case of warp travel, they are used to warp space-time around the ship and propel it at faster than light speeds). After the energy is used, there is less matter and antimatter in the ship's stores.
Whether it is fuel as we understand it or not, there would have to be something consumed or altered to generate power. Otherwise it would violate the law of conservation of matter/energy--matter/energy can neither be created nor destroyed (but it can be converted). I always assumed that the ship had to refuel at starbases occasionally, and that it just happened in the background. After all, is refueling dramatically interesting? In a lot of road trip movies you never see the travelers gas up, but it's understood that they are stopping occasionally to do so.
Higher speeds would mean more and less efficient fuel consumption--for example, when driving a car, you lose a lot of fuel efficiency when you drive around at 140 km/hr (around 85-90 mph). You get much better gas mileage if you drive around 90 km/hr (55 mph), and in fact during the energy crisis in the '70s the speed limits in the US were reduced to 55 mph because of this. We tend to prefer to make good time rather than conserve fuel because, despite our complaining about fuel cost, it's still not expensive enough for us to worry about, and there are gas stations everywhere. But if you are traveling light years through a hostile vacuum and using something like antimatter for fuel (which is pretty tough to create in large quantities), you would want to be careful to conserve it as much as possible. Plus, it might damage the engines as others have mentioned, and it might just be more dangerous--if an interstellar obstacle like a black hole or something appears suddenly you would have less time to avoid it, it might be harder for the engineers to keep things stable and safe (I believe that warp drives require quite a bit of care to run--they certainly seem to require large numbers of crewmen), etc.
Bottom line: you can run a lot faster than you can walk, but you generally walk unless you have a good reason to run--you're in a hurry, you're trying to escape from something or catch something, etc. If you ran everywhere, you'd be tired, you'd have to eat a lot more, and in many cases you really wouldn't save that much time, or need to save that much time. Running from one side of a room to another only saves a few seconds, and even if you are going further and could save a few minutes, who can't spare a few minutes in most circumstances?
